Lady Shirley Williams has become the first senior Liberal Democrat to break ranks and come out against the idea of her party striking a formal coalition deal with David Cameron, warning that it is not in the "Conservatives' DNA" to move properly in key areas.

Speaking to the Guardian, she said she would prefer the Lib Dems to agree to vote through key Tory bills rather than become coalition partners.

Asked if she thought an alliance was a good idea, she said: "No. Instead I think it would be better for us to offer them 'confidence and supply' and let them govern as a minority government, coupled with cross-party work in two areas: we need swift cross-party action to bring down the deficit, and action on political reform."

She called for an all party committee on political reform, chaired or advised by the former MP Tony Wright, who left the House of Commons this year after chairing a respected committee on the reform of parliament and whose recommendations met with varied success including some of its elements opposed by the government.

She recommended that it should include the speaker and deputy speaker of the house, as well as Scottish MPs, and it should report within a month. Williams also thinks that any cross-party committee to bring down the deficit should be modelled on a proposal made by her in the run-up to the election, for a council for financial stability in which all parties work and on which economic spokesmen from all parties should be included.

Talks between the Lib Dems and the Conservatives began this morning at 11am in the Cabinet Office, after the leaders of the two parties met for a 70-minute conversation at Admiralty House last night. Yesterday, Nick Clegg took soundings from his parliamentary party and his federal executive – both groups whose support he would have to secure in a vote with a three-quarters majority if he were to take the Lib Dems into a coalition, or anything that endangered the party's independence. The Tory leader has so far managed without taking formal soundings from his party but he will meet them tomorrow evening.

While it is not a surprise that Williams, a former Labour minister, has come out against her party forming an official coalition with the Tories, her party has been very tightly whipped in the last 72 hours, with even normally outspoken MPs, such as the Lib Dem climate change spokesman, Simon Hughes, not speaking out publicly aginst a Lib-Con deal.

Williams was particularly concerned that there has so far been no talk of securing the composition of the United kingdom. She said: "I am very concerned that preventing the break-up of the union has played no part in the negotiation between the Tories and Lib Dems.

"The Tory party made no gains to speak of in Scotland in this election … and recently, the Tories have been talking almost entirely about England. My sense is that negotiations cannot conclude without it being made clear how to keep the nation together, because if we do make a deal with the Tories, we are handing Scotland to the SNP on a plate."

She went on: "I am also concerned about the Tories' record on equality. Inequality did widen during the years of New Labour but the record was even worse under the last Tory government, and I don't see much indication that this fact is being taken into account in these negotiations either."